A quasi-linear irreducibility test in K[[x]][y]

We provide an irreducibility test in the ring K [ [ x ] ] [ y ] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input polynomial F is square-free and K is a perfect field of characteristic not dividing deg ( F ) . The algorithm uses the theory of approximate...

Full description

Saved in:
Bibliographic Details
Published in:Computational complexity Vol. 31; no. 1
Main Authors: Poteaux, Adrien, Weimann, Martin
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2022
Springer Nature B.V
Springer Verlag
Subjects:
Algebraic Geometry
Algorithm Analysis and Problem Complexity
Algorithms
Computational Mathematics and Numerical Analysis
Computer Science
Mathematics
Polynomials
Symbolic Computation
Newton polygon
68W30
11S05
Irreducibility test
Residual polynomial
Approximate roots
14H20
13P05
Algorithm
Puiseux series
Complexity
14B05
ISSN:1016-3328, 1420-8954
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We provide an irreducibility test in the ring K [ [ x ] ] [ y ] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input polynomial F is square-free and K is a perfect field of characteristic not dividing deg ( F ) . The algorithm uses the theory of approximate roots and may be seen as a generalisation of Abhyankar's irreducibility criterion to the case of non-algebraically closed residue fields.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-022-00221-w